How do you solve the inequality #8c-(c-5)>c+17#?

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Answer 1 · 2017-01-21T22:23:21

See the entire solution process below:

First, combine like terms on the left side of the inequality:

#8c - (c - 5) > c + 17#

#8c - c + 5 > c + 17#

#7c + 5 > c + 17#

Next, subtract #color(red)(c)# and #color(blue)(5)# from each side of the inequality to isolate the #c# term while keeping the equation balanced:

#7c + 5 - color(red)(c) - color(blue)(5) > c + 17 - color(red)(c) - color(blue)(5)#

#7c - color(red)(c) + 5 - color(blue)(5) > c - color(red)(c) + 17 - color(blue)(5)#

#6c + 0 > 0 + 17 - color(blue)(5)#

#6c > 12#

Now, divide each side of the inequality by #color(red)(6)# to solve for #c# while keeping the inequality balanced:

#(6c)/color(red)(6) > 12/color(red)(6)#

#(color(red)(cancel(color(black)(6)))c)/cancel(color(red)(6)) > 2#

#c > 2#